Tài liệu Circuits & Electronics P16 pptx
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6.002
CIRCUITS
AND
ELECTRONICS
Sinusoidal Steady State
6.002 Fall 2000 Lecture
16
1
Review
We now understand the why of:
5V
C
R
L
v
Today, look at response of networks
to sinusoidal drive.
Sinusoids important because signals can be
represented as a sum of sinusoids. Response to
sinusoids of various frequencies -- aka frequency
response -- tells us a lot about the system
6.002 Fall 2000 Lecture
16
2
Motivation
For motivation, consider our old friend,
the amplifier:
S
V
v
O
v
i
C
v
+
–
+
–
GS
C
R
V
BIAS
Observe v
o
amplitude as the frequency of the
input v
i
changes. Notice it decreases with
frequency.
Also observe v
o
shift as frequency changes
(phase).
Need to study behavior of networks for
sinusoidal drive.
Demo
6.002 Fall 2000 Lecture
16
3
Sinusoidal Response of RC Network
Example:
+
–
R
i
C
+
v
I
v
C
–
v
I
(
t
)
= V
i
cos
ω
t
for
t ≥
0 (
V
i
real)
= 0
for
t <
0
v
C
(0)
=
0
for
t =
0
I
v
0
t
6.002 Fall 2000 Lecture
16
4
1
1
1
1
e
c
t
u
r
Example:
+
–
R
Our Approach
i
C
+
v
I
v
C
–
Determine v
C
(t)
I
nd
u
l
g
e
m
e
!
Effort
l
e
c
t
u
r
e
sneaky approach
very
sneaky
Usual
approach
agony
easy
t
e
0
:
0
:
0
0
2
1
0
:
2
l
s
hi
T
t
x
e
N
6.002 Fall 2000 Lecture
16
5
Let’s use the usual approach…
1
Set up DE.
2
Find
v
p
.
3
Find
v
H
.
4
v
C
=
v
P
+
v
H
, solve for unknowns
using initial conditions
6.002 Fall 2000 Lecture
16
6
Usual approach…
1
Set up DE
RC
dv
C
+
v
C
=
v
I
dt
=
V
i
cos
ω
t
That was easy!
6.002 Fall 2000 Lecture
16
7
